A known type of intervertebral disc prosthesis (WO 01/01893) has two metal cover plates and a polyethylene prosthesis core which forms a pair of slide surfaces with one of the two cover plates and is fixed on the other cover plate. For this fixing, the cover plate is provided with edge ridges whose undercut connection profile cooperates with a complementary connection profile on the underside of the prosthesis core. On the right and left lateral edges of the cover plate and of the prosthesis core, such connection profiles are provided parallel to one another. In addition, there is one such profile running in a straight line on the dorsal edge of the cover plate and of the prosthesis core. There is no such profile on the ventral edge, with the result that the prosthesis core can be pushed into the connection profiles of the cover plate from the ventral direction. The prosthesis core is secured in the assembled position by a pair of locking elements provided on the ventral edge. Although the connection profiles are produced almost free of play, an important concern in prosthesis production is to ensure that, even in the case of production tolerances, it is possible to rule out any movement of the prosthesis core relative to the cover plate holding it. In particular, rotation movements of the prosthesis core relative to the cover plate holding it must be ruled out. The invention has recognized that this can be improved not only by precision production but also by a special arrangement of the connection profiles.